Abstract
In this paper, pinning control of a class of asymmetrically coupled complex dynamical network with heterogeneous delays is studied. Two kinds of controllers, adaptive controllers and linear feedback controllers, are presented and the Jordan canonical transformation method is used instead of the matrix diagonalization method. Therefore, it is not necessary for some relevant matrices to be diagonalizable. Moreover, a simply approximate formula is provided to estimate how many and which nodes should a network with fixed network structure and coupling strength be pinned to reach synchronization. Here, the inner-coupling matrix is not necessarily symmetric. One example is given to show the effectiveness of the proposed synchronization criteria.
This work was supported by the National Natural Science Foundation of China under Grant No. 61104031.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Song, Q., Cao, J., Yu, W.: Second-order leader-following consensus of nonlinear multi-agents via pinning control. Syst. & Cont. Lett. 59, 553–562 (2010)
Yu, W., Chen, G., Lü, J.: On pinning synchronization of complex dynamical networks. Automatica 45(2), 429–435 (2009)
Wu, J., Jiao, L.: Synchronization in complex delayed dynamical networks with nonsymmetric coupling. Physica A 386, 513–530 (2007)
Wu, J., Jiao, L.: Synchronization in complex dynamical networks with nonsymmetric coupling. Physica D 237(19), 2487–2498 (2008)
Wang, X., Chen, G.: Pinning control of scale-free dynamical networks. Physica A 310(3-4), 521–531 (2002)
Xiang, L., Liu, Z., Chen, Z., Chen, F., Yuan, Z.: Pinning control of complex dynamical networks with general topology. Physica A 379, 298–306 (2007)
Liu, Z.X., Chen, Z.Q., Yuan, Z.Z.: Pinning control of weighted general complex dynamicalnetworks with time delay. Physica A 375, 345–354 (2007)
Zhou, J., Lu, J., Lü, J.: Pinning adaptive synchronization of a general complex dynamical network. Automatica 44, 996–1003 (2008)
Xiang, L., Chen, Z., Liu, Z., Chen, F., Yuan, Z.: Pinning control of complex dynamical networks with heterogeneous delays. Computers and Mathematics with Applications 56, 1423–1433 (2008)
Li, C.P., Sun, W.G., Kurths, J.: Synchronization of complex dynamical networks with time delays. Physica A 361, 24–34 (2006)
Williams, R.J., Martinez, N.D., Berlow, E.L., Dunne, J.A., Barabasi, A.-L.: Two degrees of separation in complex food webs. Proc. Natl. Acad. Sci. 99, 12913–12916 (2002)
Vidyasagar, F.: Nonlinear Systems Analysis. Prentice-Hall, Englewood Cliffs (1978)
Horn, R.A., Johnson, C.R.: Topics in Matrix Analysis. Post & Telecom Press, China (2005)
Gopalsamy, K.: Stability and Oscillations in Delay Differential Equations of Population Dynamics. Kluwer Academic, Dordrecht (1992)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Ren, F., Zhao, H. (2014). Pinning Control of Asymmetrically Coupled Complex Dynamical Network with Heterogeneous Delays. In: Huang, DS., Jo, KH., Wang, L. (eds) Intelligent Computing Methodologies. ICIC 2014. Lecture Notes in Computer Science(), vol 8589. Springer, Cham. https://doi.org/10.1007/978-3-319-09339-0_80
Download citation
DOI: https://doi.org/10.1007/978-3-319-09339-0_80
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-09338-3
Online ISBN: 978-3-319-09339-0
eBook Packages: Computer ScienceComputer Science (R0)